Common Sense Reasoning in Diagnostic Systems - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 114

For each of these points we calculate the information quantity as follows:
QuanN(R3) =1 + 1 + 2/2 = 3
QuanN(Rl) =1 + 1+2/2 = 3
QuanN(06) =1 + 1=2
QuanN(05) =1+2/2+1 + 1=4
QuanN(04) =1 + 1=2
QuanN(03) = 1 + 1 = 2
QuanN(02) = 1 + 2/2+1 + 1 + 1 + 1 = 6
QuanN(Ol) = 1 + 1=2
Points with the greatest value of function QuanN(x) have the greatest priority of a choice.
We will call the given method of choosing a measuring point as SIEH (Supporting and
Inconsistent Environment Heuristics).
One can see that the point 02 as the most informative is again offered. And in the given
approach the difference in information quantity between various points is expressed more
brightly than without Nogood usage.

7.4 Knowledge about coincided assumptions of the inconsistent environments
During diagnostics of faulty devices as a result of confirmations and refutations of some
predictions there is a modification of a set of inconsistent environments Nogood.
In each component set from Nogood one or more components are broken what was a reason
of including a supporting set into the inconsistent environments Nogood. Taking the
intersection of all sets of the inconsistent environments, we receive a set of components
which enter into each of them, so their fault can be a reason explaining an inconsistence of
each set holding in Nogood. Thus, we obtain the list of components a state of which is
recommended to test first of all, i.e. the most probable candidates on faultiness.
The set intersection of inconsistent environments is expressed by the following equation:

 
i

SingleNogood E

i

E  Nogood

For Nogood = {{And2, Invl}, {And2, Inv2, Inv5}, {And2, Inv3}} the set of the most probable
candidates will be the following: SingleNogood = {And2}.
If SingleNogood = , it means that there are some disconnected faults. In this case the given
approach is inapplicable and it is necessary to define more precisely the further information
by any other methods.
After obtaining a set SingleNogood ≠ , on the base of environments of value predictions in
device points it is necessary to select those measurement points that allow to effectively test
components to be faulted from SingleNogood.
For this purpose we will work with the sets obtained as a result of an intersection of each
environment from Envs(x) with SingleNogood:

Envs(x)  SingleNogood = {J  SingleNogood : J  Envs{x)}

The following versions are possible:
a.  J  Envs(x): J  SingleNogood . One of environments of the value prediction in the point
x coincides with the set SingleNogood. The given version allows to test faulty
components from the set SingleNogood most effectively so this measurement point x
is selected with the most priority.